414 
MR, S. H. BURBURY ON THE COLLISION OE ELASTIC BODIES. 
The equations given by Professor Burnside can easily be modified so as to meet the 
case of elastic bodies of any shape. 
11. It would not be difficult to extend the method of (8) and show that the 
Maxwell-Boltzmann distribution is a necessary, as well as a sufficient condition for 
stationary motion. But that is more completely done by following or extending 
Boltzmann’s method. 
Let there be a set of systems which we will call systems M, whose co-ordinates and 
velocities are . . . p r and /q . . . p r . 
Let the number of such systems for which at any instant the co-ordinates lie 
between the limits 
Pi and pi + dpi' 
. > 
p r and p r + dp r _ 
• ■ (A). 
and the velocities between the limits 
be 
or, shortly, 
lh and pi + dpi 
. > . 
pr and pr -f dp f . __ 
¥ (pi ... p r pi .. . p^ dpi . . . dp r dpi . . . dp r , 
¥dpi . . . dp,, dpi . . . dp,-. 
(A'), 
Let there be another set of systems, which we will call systems m, whose co¬ 
ordinates ar e p > r +1 ■ ■ • pit and velocities + 1 . . . p». 
And let the number of systems m for which at any instant the coordinates lie 
between the limits 
pr + i and £>,•+] -f- dp r + 1 
.> 
pit and p„ + dp„ 
(B), 
and the velocities between the limits 
be 
p y+l and pr+i + dp,. + i 
p„ and p„ + dp„ 
f ( P r + 1 ■ • ■ _Pr + 1 • • • pn) dp r+ 1 . . . dp„ dp r+ i . . . dp n 
(n 
